Unexpected behavior in R using lapply() with glm() and cv.glm() - r

Question

I am trying to apply cross validation to a list of linear models and getting an error.
Here is my code:
library(MASS)
library(boot)
glm.fits = lapply(1:10,function(d) glm(nox~poly(dis,d),data=Boston))
cvs = lapply(1:10,function(i) cv.glm(Boston,glm.fits[[i]],K=10)$delta[1])
I get the error:
Error in poly(dis, d) : object 'd' not found
I then tried the following code:
library(MASS)
library(boot)
cvs=rep(0,10)
for (d in 1:10){
glmfit = glm(nox~poly(dis,d),data=Boston)
cvs[d] = cv.glm(Boston,glmfit,K=10)$delta[1]
}
and this worked.
Can anyone explain why my first attempt did not work, and suggest a fix?
Also, assuming a fix to the first attempt can be obtained, which way of writing code is better practice? (assume that I want a list of the various fits and that I would edit the latter code to preserve them) To me, the first attempt is more elegant.

Answer 1

In order for your first attempt to work, cv.glm (and maybe glm) would have to be written differently to take much more care about where evaluations are taking place.
The function cv.glm basically re-evaluates the model formula a bunch of times. It takes that model formula directly from the fitted glm object. So put yourself in R's shoes (as it were), and consider you're deep in the function cv.glm and you've been instructed to refit this model:
glm(formula = nox ~ poly(dis, d), data = Boston)
The fitted glm object has Boston in it, and glm knows to look first in Boston for variables, so it finds nox and dis easily. But where is d? It's not in Boston. It's not in the fitted glm object (and glm wouldn't know to look there anyway). In fact, it isn't anywhere. That d value existed only in the context of the lapply iterations and then disappeared.
In the second case, since d is currently an active variable in your for loop, after R fails to find d in the data frame Boston, it looks in the parent frame, in this case the global environment and finds your for loop index d and merrily keeps going.
If you need to use glm and cv.glm in this way I would just use the for loop; it might be possible to work around the evaluation issues, but it probably wouldn't be worth the time and hassle.